In a VCL TMemo, if you try to read from a line index that doesn't exist then the output string will be blank, and if you try to write to a line index that doesn't exist then the input string will be ignored. No errors are raised. So, in your case, for example, if you try to write to Memo1.Lines[2] when Memo1 does not have at least 3 lines, then your LblLastName.Caption string will be ignored.
So, like Brian said, you have to make sure a given line actually exists before you can read/write it.
That being said, using a TMemo probably isn't the best choice for this task to begin with. Why not use 3 TEdit's instead? Or maybe a TStringGrid, or a TValueListEditor, or an editable TListView instead? There are many choices, depending on your UI needs.